85162 - Differential Calculus

Academic Year 2025/2026

Learning outcomes

By the end of the course the student learns the basic concepts and techniques of multivariate differential calculus. More specifically, the student is able to calculate partial derivatives, to find maxima and minima and to use the Lagrange multiplicator method.

Course contents

Basic properties of the Euclidean space. Partial derivatives and differentiable functions. Critical points. Derivation of composite functions. Multivariate Taylor’s formula. Hessian matrices. Critical points analysis. Implicit functions: Dini’s theorem. Submanifold of the Euclidean space . Critical points on submanifolds.

Readings/Bibliography

Material provided by the teacher

Teaching methods

Frontal lessons

Assessment methods

The examination consists of an oral examination. Will occur 'the student's competency both in terms of acquisition of concepts and methods, with application to concrete cases.

Teaching tools

Software "maxima"

Office hours

See the website of Sergio Venturini